We discussed this at length in the TWD forum and I think even Chris Hardwick discussed it on The Talking Dead. In an unsupervised coma 2 weeks would be pushing it in terms of survival without fluids. So max, 2 weeks after the last IV bag runs dry.
On AMC.com, there is a webisode that explains where the painted warning on the cafeteria doors in the hospital came from...the Dr that gets killed in the webisode was probably keeping Rick alive and even in a chemical induced coma. When she gets shot, he wakes up not long afterward.